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Range of the Coefficient of Determination
The coefficient of determination ranges from 0 to 1. 0 indicates that there is no linear relationship at all, 1 indicates that the relationship is perfect. What counts as a "high" or "good" coefficient varies from field to field. In psychology, 0.3 is quite high; in physics 0.8 is often considered low.
What the Coefficient Measures
The coefficient of determination measures the strength of a linear relationship. But the exact meaning of "linear relationship" is often confusing to students. A linear relationship is linear in its parameters. For example, you might model weight in human adults as a function of height and height squared, getting a regression equation such as:
W = b0 + b1*H + b2*H^2
Where W is weight and H is height and b0, b1 and b2 are coefficients to be estimated. This is a linear regression, because none of the parameter are raised to powers.
Coefficient of Determination in Analysis of Variance
In analysis of variance (ANOVA), models are developed and evaluated based on sums of squares, or variances. In any set of quantitative data that is collected on several groups, you can look at the total variance and the variance within and between groups. The coefficient of determination is the sum of squares between groups divided by the total sum of squares.
Proportion of Variation
Another way to look at the coefficient of determination is that it is the proportion of variation in the dependent variable (what we are trying to explain) that is accounted for by the model. So, if the coefficient is 0.8, it means that 80 per cent of the variation in the dependent variable is accounted for by the model.